Craig Morton led his third team, the Broncos to the SB in 1978,
his 15th year in the league. In the previous 3 years, his TD/INT ratio was 29/49. He was pretty good with the Cowboys before Staubach took over.
Many people thought Morton was done. But in the end, he wound up playing seven more years then Staubach.

Vince Ferragamo ratio was 7/12 the previous 3 years as a backup, but took the LA Rams to the SB in 1980.
He was 69-145 and less than a thousand yard passing in those 3 years.
A 4th round draft pick.

Jim Plunkett became the starter of the Raiders in the 6th week, then promptly went on to win the SB for them in 1981.
His passer rating in the previous 8 years never touch 70.
Plunket was a #1 pick, called "best pro quarterback prospect ever" by some, was ROY, but injuries marred the following years of his career, the next four with the Pats never having a winning record. He was traded to SF where he spent 2 ho-hum years and was released. The Raiders picked him up, the first 2 years he attempted a total of 15 passes. Then came that 3rd year.

In his second year (1981), David Woodley was splitting time with backup Don Strock in Miami.
In a playoff game against the Chargers, Woodley started and the Dolphins fell behind 0-24. Strock came in and made the game a thriller, a 38-41 OT loss.
The next year, the strike shorten season 1982 saw Woodley playing in 9 games, 1080 yd passing, a 5/8 TD/INT ratio, and a 63.5 rating. Yet he took them to the SB in Jan 83. He was an 8th round draft pick.

Jeff Hostetler was a fifth year backup for the Giants with a total of 109 pass attempts, until the 15th game of the season when he took over for an injured Phil Simms. NY went on to win the last 2 games en route to a SB victory over the Bills. He was a 3rd round draft pick.

I'm assuming you're looking at backup to starter late bloomers. I guess that could be Sage. But to assume that he is the statistical anomoly is a stretch. Like I said, there's more Commander Cody than anything in him if you ask me. And that's not a bad thing. Carlson filled in very admirably for Moon on several occasions.